Ch 21 - The chi-square test for goodness of fit Flashcards
The chi-square x² test is used when ____
It measures ____
the data are categorical
how different the observed data are from what we would expect if H0 was true.
The chi-square (c2) statistic compares
observed and expected counts.
Observed counts
are the actual number of observations of each type.
Expected counts
are the number of observations that we would expect to see of each type if the null hypothesis was true.
Large values for x² represent
strong deviations from the expected distribution under H0
will tend to be statistically significant.
The x² distributions are
a family of distributions that take only positive values, are skewed to the right, and are described by a specific degrees of freedom.
Published tables & software give the upper-tail area for critical values of many x² distributions.
Table D
The chi-square test can be used to for a categorical variable (1 SRS) with
any number k of levels.
The null hypothesis can be that all population proportions are equal (uniform hypothesis)
OR that they are equal to some specific values, as long as the sum of all the population proportions in H0 equals 1.
For 1 SRS of size n with k levels of a categorical variable
H0: P1=P2… ; Pk: ____ expected counts ___
H0: P1 = P1H0 and P2 = P2H0; Pk:____ expected counts ___
We can safely use the chi-square test when
all expected counts are 1 or more (≥1)
no more than 20% of expected counts are less than 5
(The chi-square test for goodness of fit is used when we have a single SRS from a population, and the data are categorical, with k mutually exclusive levels.)
The chi-square statistic for goodness of fit with k proportions measures _____
It follows the chi-square distribution with ____
it has the formula _____
how much observed counts differ from expected counts.
with k − 1 degrees of freedom
The individual values summed in the x² statistic are
the x² components.
When the test is statistically significant, the largest components indicate
which condition(s) are most different from the expected H0.
can also compare the actual proportions qualitatively in a graph.
A non-significant P-value is
not conclusive: H0 could be true, or not.
Not rejecting but also not saying it is true
This is particularly relevant in the X2 goodness of fit test where we are often interested in H0 that the data fit a particular model.
A significant P-value suggests _____
But finding a non-significant P-value ____
that the data do not follow that model.
is NOT a validation of the null hypothesis and does NOT suggest that the data do follow the hypothesized model. It only shows that the data are not inconsistent with the model.
